# Shared Flashcard Set

## Details

phys 486 final
uiuc w/ prof beck
44
Physics
12/14/2019

Term
 TDSE
Definition
 [image]
Term
 Probability of finding a particle between a and b at time t
Definition
 [image]
Term
 < x >
Definition
 [image]
Term
 < p > (3 definitions)
Definition
 [image][image]
Term
 < T >
Definition
 [image]
Term
 TISE
Definition
 [image]
Term
 Hamiltonian operator
Definition
 [image]
Term
 Calculating expectation values for < x > and < x^2 > shortcuts
Definition
 odd function with x -> goes to 0even function -> double and change bounds
Term
 Uncertainty principle
Definition
 [image]
Term
 E_n for infinite square well
Definition
 [image]
Term
 ψ_n inside infinite well
Definition
 [image]
Term
 c_n
Definition
 [image]f(x) is the wavefunction (generic)
Term
 [image]
Definition
 1
Term
 < H >
Definition
 [image]
Term
 Probability of states in well
Definition
 |c_n|^2
Term
 |a>
Definition
 [image]
Term
 inner product
Definition
 [image]
Term
 [image] in integral form
Definition
 [image]
Term
 Observables are represented by
Definition
 hermitian operators
Term
 Hermitian operator Q
Definition
 [image]
Term
 Eigenvalue eqn for Q operator
Definition
 Q Ψ = q ΨΨ = eigenfunctionq = eigenvalue
Term
 Integration by parts formula
Definition
 [image]
Term
 Normalizeable eigenfunctions of a hermitian operator
Definition
 are orthogonal (int f*g = 0) and their eigenvalues are real
Term
 Expectation value of Q_op
Definition
 [image]
Term
 Hilbert Space
Definition
 [image]
Term
 [x,p] =
Definition
 i hbar
Term
 Generalized uncertainty principle
Definition
 [image]
Term
 The system is initially in state (a+), and you want probability of (b-)
Definition
 [image]
Term
 Allowed energy for a hydrogen atom
Definition
 E_1/n^2
Term
 Label spacial wavefunctions for hydrogen
Definition
 [image]
Term
 [image][image][image]
Definition
 [image]
Term
 [L^2, L_(x,y,z)]
Definition
 [image]
Term
 L^2, Lz eigenvalues/fn
Definition
 [image]
Term
 Pauli Matricies
Definition
 [image]
Term
 What quantum numbers are "allowed" for a given n?
Definition
 l = 0,1,2,...,n -1m_l = -l,-l+1,...,0,...,l-1,lm_s = ±1/2
Term
 Hamiltonian in perturbation theory
Definition
 [image]
Term
 Superscripts in perturbation theory
Definition
 Order. Ex: H^0 first order
Term
 First order energy correction
Definition
 [image]This is an integral H' * Psi^2Can also be X (eigenstate)
Term
 First order wavefunction correction
Definition
 [image]
Term
 Two non interacting particles wavefunction
Definition
 [image][image]
Term
 W matrix
Definition
 [image]
Term
 Energy using W matrix
Definition
 Use formula
Term
 J
Definition
 L+S
Term
 Zeeman Effect
Definition
 Atom placed in uniform external B field
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